Ben is $20$ years older than Daniel. Ben and Daniel first met two years ago. Three years ago, Ben was $3$ times as old as Daniel. How old is Daniel now?
We can use the given information to write down two equations that describe the ages of Ben and Daniel. Let Ben's current age be $b$ and Daniel's current age be $d$. The information in the first sentence can be expressed in the following equation: ${b = d + 20}$ Three years ago, Ben was $b - 3$ years old, and Daniel was $d - 3$ years old. The information in the third sentence can be expressed in the following equation: ${b - 3 = 3(d - 3)}$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$, it might be easiest to use our first equation for $b$ and substitute it into our second equation. Our first equation is: ${b = d + 20}$. Substituting this into our second equation, we get the equation: $ {(d + 20)}{-3 = 3(d - 3)} $ which combines the information about $d$ from both of our original equations. Simplifying both sides of this equation, we get: $d + 17 = 3 d - 9$. Solving for $d$, we get: $2 d = 26$. $d = 13$.